Consider the single factor APT. Portfolio A has a beta of 0.2 and an expected return of 13%. Portfolio B has a beta of 0.4 and an expected return of 15%. The risk-free rate of return is 10%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio _________ and a long position in portfolio _________.
A) A; A
B) A; B
C) B; A
D) B; B

Question

Quizplus · Accepted Answer

According to the Arbitrage Pricing Theory (APT), the expected return on a portfolio should be linearly related to its beta with respect to the market. The formula to calculate the expected return is: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). If we rearrange the formula to solve for the market return, we can compare the expected returns of both portfolios to see if they align with the APT. For Portfolio A: 13% = 10% + 0.2 * (Market Return - 10%)For Portfolio B: 15% = 10% + 0.4 * (Market Return - 10%)Solving these equations, we find that the expected market return implied by Portfolio A is higher than that implied by Portfolio B. This discrepancy suggests an arbitrage opportunity. To exploit this, one should short the portfolio that is overpriced (higher beta but lower than expected return) and go long on the portfolio that is underpriced (lower beta but higher than expected return). In this case, Portfolio B is overpriced relative to its expected return based on its beta, and Portfolio A is underpriced. Therefore, you should take a short position in Portfolio B and a long position in Portfolio A to exploit the arbitrage opportunity.

Consider the Single Factor APT